Question: Simplify to lowest terms. $\dfrac{24}{32}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 24 and 32? $24 = 2\cdot2\cdot2\cdot3$ $32 = 2\cdot2\cdot2\cdot2\cdot2$ $\mbox{GCD}(24, 32) = 2\cdot2\cdot2 = 8$ $\dfrac{24}{32} = \dfrac{3 \cdot 8}{ 4\cdot 8}$ $\hphantom{\dfrac{24}{32}} = \dfrac{3}{4} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{24}{32}} = \dfrac{3}{4} \cdot 1$ $\hphantom{\dfrac{24}{32}} = \dfrac{3}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{24}{32}= \dfrac{2\cdot12}{2\cdot16}= \dfrac{2\cdot 2\cdot6}{2\cdot 2\cdot8}= \dfrac{2\cdot 2\cdot 2\cdot3}{2\cdot 2\cdot 2\cdot4}= \dfrac{3}{4}$